Inequalities in Hilbert Modules of Matrix-Valued Functions

DOI10.2307/2043849zbMath0493.46023OpenAlexW4239804985MaRDI QIDQ3955903

Adhemar Bultheel

Publication date: 1982

Full work available at URL: https://doi.org/10.2307/2043849

zbMATH Keywords

optimizationgeneralized inversereproducing kernelsmatrix valued functionsHilbert modules of matrix-valued functionsmatrix valued nonnegative hermitian sesquilinear functionmatrix version of the Cauchy-Schwarz inequalitymultivariate filtering problems

Mathematics Subject Classification ID

Inference from stochastic processes and prediction (62M20) Filtering in stochastic control theory (93E11) Hilbert spaces of continuous, differentiable or analytic functions (46E20) Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX) (46H25) Linear spaces of operators (47L05) Inner product spaces and their generalizations, Hilbert spaces (46C99)

Related Items (8)

On a class of extremal solutions of a moment problem for rational matrix-valued functions in the nondegenerate case. II ⋮ Time-invariant restrictions of volatility functionals: efficient estimation and specification tests ⋮ On a moment problem for rational matrix-valued functions. ⋮ Extremal problems for matrix-valued polynomials on the unit circle and applications to multivariate stationary sequences. ⋮ Optimal input design for direct data-driven tuning of model-reference controllers ⋮ On Hilbert modules of rational matrix-valued functions and related inverse problems ⋮ On a class of extremal solutions of a moment problem for rational matrix-valued functions in the nondegenerate case I ⋮ On Canonical Solutions of a Moment Problem for Rational Matrix-valued Functions

Cites Work

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• The prediction theory of multivariate stochastic processes. I. The regularity condition. - II. The linear predictor
• The square-integrability of matrix-valued functions with respect to a non-negative Hermitian measure
• The Nevanlinna–Pick Problem for Matrix-Valued Functions
• Lossless chain scattering matrices and optimum linear prediction: The vector case
• Orthogonal polynomial matrices on the unit circle
• Theory of Reproducing Kernels

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